Аннотация:An appropriate mathematical model is needed to study areal process or system. Dealing with such probability theory applicationsas communication, reliability, queueing, inventory, finance, insurance andmany others, a researcher usually considers input-output models.Modernperiod in actuarial sciences is characterized by consideration of complexsystems, interplay of cost and reliability approaches and wide use of computers,therefore it is desirable to treat discrete-time models. They cangive approximation to corresponding continuous-time ones. Moreover,in some cases they provide a better description of a real-life situation.So, we consider three discrete-time models and investigate their optimalperformance and stability.